This evening I came across a passage in the Summa Theologica demonstrating the point that such an approach is not at all doomed to failure.
Augustine says (Retract. i, 4): "I do not approve having said in the prayer, O God, Who dost wish the sinless alone to know the truth; for it may be answered that many who are not sinless know many truths." Now man is cleansed from sin by grace, according to Psalm 50:12: "Create a clean heart in me, O God, and renew a right spirit within my bowels." Therefore without grace man of himself can know truth.So we see that St. Thomas teaches the natural gifts God has given us - namely, reason and the senses - are sufficient for us to acquire knowledge (that is to say, we may learn truth), with the major exception of those things which can only be known by the grace of faith. Of course, it is another question entirely what extent of knowledge is available to us by natural means; St. Thomas provides us some "small" (!) idea of his judgment thereof in the SCG.
I answer that, To know truth is a use or act of intellectual light, since, according to the Apostle (Ephesians 5:13): "All that is made manifest is light." Now every use implies movement, taking movement broadly, so as to call thinking and willing movements, as is clear from the Philosopher (De Anima iii, 4). Now in corporeal things we see that for movement there is required not merely the form which is the principle of the movement or action, but there is also required the motion of the first mover. Now the first mover in the order of corporeal things is the heavenly body. Hence no matter how perfectly fire has heat, it would not bring about alteration, except by the motion of the heavenly body. But it is clear that as all corporeal movements are reduced to the motion of the heavenly body as to the first corporeal mover, so all movements, both corporeal and spiritual, are reduced to the simple First Mover, Who is God. And hence no matter how perfect a corporeal or spiritual nature is supposed to be, it cannot proceed to its act unless it be moved by God; but this motion is according to the plan of His providence, and not by necessity of nature, as the motion of the heavenly body. Now not only is every motion from God as from the First Mover, but all formal perfection is from Him as from the First Act. And thus the act of the intellect or of any created being whatsoever depends upon God in two ways: first, inasmuch as it is from Him that it has the form whereby it acts; secondly, inasmuch as it is moved by Him to act.
Now every form bestowed on created things by God has power for a determined act, which it can bring about in proportion to its own proper endowment; and beyond which it is powerless, except by a superadded form, as water can only heat when heated by the fire. And thus the human understanding has a form, viz. intelligible light, which of itself is sufficient for knowing certain intelligible things, viz. those we can come to know through the senses. Higher intelligible things the human intellect cannot know, unless it be perfected by a stronger light, viz. the light of faith or prophecy which is called the "light of grace," inasmuch as it is added to nature.
Hence we must say that for the knowledge of any truth whatsoever man needs Divine help, that the intellect may be moved by God to its act. But he does not need a new light added to his natural light, in order to know the truth in all things, but only in some that surpass his natural knowledge. And yet at times God miraculously instructs some by His grace in things that can be known by natural reason, even as He sometimes brings about miraculously what nature can do. [ST I-II, Q109, A1; emphasis added]